Large/small eddy simulations: A posteriori analysis in high Reynolds number isotropic turbulence

TL;DR

This paper demonstrates that Large/Small Eddy Simulation (L/SES) can accurately replicate high Reynolds number turbulence properties with significantly reduced computational cost compared to DNS, enabling practical high-fidelity flow simulations.

Contribution

The study introduces and validates L/SES as an efficient hybrid turbulence modeling approach that maintains DNS-level accuracy at a fraction of the computational expense.

Findings

L/SES closely matches DNS in turbulence statistics and small-scale properties.

Optimal parameters for L/SES are systematically identified.

L/SES reduces computational cost by about three orders of magnitude.

Abstract

While direct numerical simulations (DNS) are the most accurate method for studying turbulence, their large computational cost restricts their use to idealized configurations and to Reynolds numbers well below those found in practical systems. A recently proposed method, Large/Small Eddy Simulation (L/SES), aims to overcome this limitation while still providing the solution fidelity comparable to that of DNS. L/SES represents a pair of coupled calculations: a lower-fidelity Large Eddy Simulation (LES), which captures the large-scale flow structure, and a high-fidelity Small-Eddy Simulation (SES) targeting a sub-region of interest of the LES, in which the small-scale dynamics is fully resolved. In this study, we demonstrate the accuracy and performance of L/SES in large Reynolds-number homogeneous isotropic turbulence (HIT) up to Taylor-scale Reynolds number approximately 600. Turbulence properties obtained with L/SES are shown to be in close agreement with the literature, both in terms of global characteristics, such as kinetic energy spectra and dissipative anomaly, as well as small-scale properties, such as higher-order moments of the velocity gradients up to the 10th order and probability density functions of the intermittent quantities. Also using simulations of HIT, we systematically investigate various method parameters and determine their optimal converged values. Finally, we discuss the computational cost of L/SES and demonstrate that it is approximately 3 orders of magnitude lower than for a traditional DNS at the highest Reynolds number considered here. This highlights the potential of L/SES as a discovery tool, which brings high-fidelity simulations of realistic flows into the realm of feasibility.